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Stericated 7-cubes

Orthogonal projections in B6 Coxeter plane
[[File:7-cube t0 B6.svg160px]]7-cube
[[File:7-cube t014 B6.svg160px]]Steritruncated 7-cube
[[File:7-cube t135 B6.svg160px]]Bistericantellated 7-cube
[[File:7-cube t034 B6.svg160px]]Steriruncinated 7-cube
[[File:7-cube t1245 B6.svg160px]]Bisteriruncitruncated 7-cube

In seven-dimensional geometry, a stericated 7-cube is a convex uniform 7-polytope with 4th-order truncations (sterication) of the regular 7-cube.

There are 24 unique sterication for the 7-cube with permutations of truncations, cantellations, and runcinations. 10 are more simply constructed from the 7-orthoplex.

This polytope is one of 127 uniform 7-polytopes with B7 symmetry.

Stericated 7-cube

Stericated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Small cellated hepteract (acronym: ) (Jonathan Bowers)

Images

Bistericated 7-cube

bistericated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Small bicellated hepteractihecatonicosoctaexon (acronym: ) (Jonathan Bowers)

Images

Steritruncated 7-cube

steritruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Cellitruncated hepteract (acronym: ) (Jonathan Bowers)

Images

Bisteritruncated 7-cube

bisteritruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Bicellitruncated hepteract (acronym: ) (Jonathan Bowers)

Images

Stericantellated 7-cube

Stericantellated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Cellirhombated hepteract (acronym: ) (Jonathan Bowers)

Images

Bistericantellated 7-cube

Bistericantellated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Bicellirhombihepteract (acronym: ) (Jonathan Bowers)

Images

Stericantitruncated 7-cube

stericantitruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Celligreatorhombated hepteract (acronym: ) (Jonathan Bowers)

Images

Bistericantitruncated 7-cube

bistericantitruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Bicelligreatorhombated hepteract (acronym: ) (Jonathan Bowers)

Images

Steriruncinated 7-cube

Steriruncinated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Celliprismated hepteract (acronym: ) (Jonathan Bowers)

Images

Steriruncitruncated 7-cube

steriruncitruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Celliprismatotruncated hepteract (acronym: ) (Jonathan Bowers)

Images

Steriruncicantellated 7-cube

steriruncicantellated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Celliprismatorhombated hepteract (acronym: ) (Jonathan Bowers)

Images

Bisteriruncitruncated 7-cube

bisteriruncitruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Bicelliprismatotruncated hepteractihecatonicosoctaexon (acronym: ) (Jonathan Bowers)

Images

Steriruncicantitruncated 7-cube

steriruncicantitruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Great cellated hepteract (acronym: ) (Jonathan Bowers)

Images

Bisteriruncicantitruncated 7-cube

bisteriruncicantitruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Great bicellated hepteractihecatonicosoctaexon (Acronym ) (Jonathan Bowers)

Images

Notes

References

  • H.S.M. Coxeter:
    • H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
    • Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, wiley.com,
      • (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10]
      • (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
      • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
  • Norman Johnson Uniform Polytopes, Manuscript (1991)
    • N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
  • x3o3o3o3x3o4o - , x3o3x3o3x3o4o - , x3x3o3o3x3o4o - , o3x3x3o3o3x4o - , x3o3x3o3x3o4o - , o3x3o3x3o3x4o - , x3x3x3o3x3o4o - , o3x3x3x3o3x4o - , x3o3o3x3x3o4o - , x3x3x3o3x3o4o - , x3o3x3x3x3o4o - , o3x3x3o3x3x4o - , x3x3x3x3x3o4o - , o3x3x3x3x3x4o -

References

  1. Klitizing, (x3o3o3o3x3o4o - )
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  4. Klitizing, (o3x3x3o3o3x4o - )
  5. Klitizing, (x3o3x3o3x3o4o - )
  6. Klitizing, (o3x3o3x3o3x4o - )
  7. Klitizing, (x3x3x3o3x3o4o - )
  8. Klitizing, (o3x3x3x3o3x4o - )
  9. Klitizing, (x3o3o3x3x3o4o - )
  10. Klitizing, (x3x3x3o3x3o4o - )
  11. Klitizing, (x3o3x3x3x3o4o - )
  12. Klitizing, (o3x3x3o3x3x4o - )
  13. Klitizing, (x3x3x3x3x3o4o - )
  14. Klitizing, (o3x3x3x3x3x4o - )
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